I quote a paragraph from the WSJ today on China's not too successful attempts to build low cost housing.
Local governments prefer to sell land to developers for middle-to-high-end apartment construction, as this pulls in more revenue for them. Private developers prefer it this way, too, as they can usually achieve better margins by selling apartments for the top end of the market.
Again and again, it is the incentives and not the market which decides. It was childishly naive to not expect the wealth gap not to narrow everywhere. I have always been skeptical of this. I recall how dismayed I was when they repealed the Glass-Steagal Act in the US.